Triple-layer model 385 intrinsic constants

TABLE 10.12. Triple-layer model intrinsic constants for adsorption by both amorphous hydrous ferric oxide (HFO) and goethite (a-FeOOH)... 

Some triple layer model intrinsic equilibrium constants for surface complexation in the o-plane are Eqs. (6.10) to (6.13) as in the constant capacitance model, where h is replaced by 1, . Possible intrinsic equilibrium constants for surface complexation in the (3-plane are... 

Corresponding to these four conditional constants are the triple layer model intrinsic equilibrium constants ... 

Some stability constants for ion pairs on Fe oxides are listed in Table 10.4. This model was applied by Davis and Leckie (1978, 1980) to adsorption of various cations and anions on ferrihydrite. The extended triple layer model of Sahai and Svenjensky (1997) incorporates recent advances in aqueous electrolyte chemistry which enable aqueous activity coefficients for electrolytes to be calculated over a wide range of ionic strengths. The model also considers the free energy of adsorption of an ion to be the sum of the contributions from an electrostatic term, a Born solvation term and a ion intrinsic term. This extended model has been applied to adsorption of Co and Cd on goethite. 

The following adsorption reactions and intrinsic constants are available for the triple-layer model, where FeO", FeOH, and FeOHJ are surface sites. 

In the triple layer model, values for the intrinsic protonation and dissociation constants, as well as values for tlie intrinsic surface complexation constants for the background electrolyte, can be obtained from hnear, double, or electrokmetic extrapolations to zero surface charge and zero and infinite electrolyte concentration. Values of intrinsic protonation-dissociation constants and intrinsic surface complexation constants for background electrolytes obtamed for the triple layer model using the various extrapolations are compiled in Goldberg (1992). Use of graphical extrapolation methods has been criticized because the triple layer parameter values obtained are not unique (Koopal et al., 1987). 

Just as in the constant capacitance model, the intrinsic equilibrium constant in the triple layer model reters to an unconventional standard state wherein the complexed species create no coulombic effects, i.e., = K when (J4om = 0. 

When represents a metal cation not in the background electrolyte, the intrinsic constants are determined by fitting the triple layer model to adsorption edge data. This fitting entails a surface speciation calculation with previously measured values of the intrinsic constants in Eq. 5.61, the capacitance parameters Ci and C2, and the parameter Af. The computation includes Eqs. 5.58, 5.59, and 5.69, as well as surface charge and mole balance equations imposed as constraints. " ... 

Recently, the extended triple layer model (ETLM) was introduced by Sveijensky and coworkers (Sverjensky 2005 Sveijensky and Fukushi 2006), incorporating prediction of intrinsic equilibrium constants based on crystal chemical, electrostatic, and thermodynamic theory, allowing the reduction of adjustable parameters. In the ETLM, proton sorption Reactions 12.2 and 12.3 are written as associations ... 

Gouy-Chapman, Stern, and triple layer). Methods which have been used for determining thermodynamic constants from experimental data for surface hydrolysis reactions are examined critically. One method of linear extrapolation of the logarithm of the activity quotient to zero surface charge is shown to bias the values which are obtained for the intrinsic acidity constants of the diprotic surface groups. The advantages of a simple model based on monoprotic surface groups and a Stern model of the electric double layer are discussed. The model is physically plausible, and mathematically consistent with adsorption and surface potential data. 

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